**David Rezza Baqaee and Emmanuel Farhi**: *The Microeconomic Foundations of Aggregate Production Functions*: "We provide a general methodology for analyzing...aggregate production functions by deriving their first- and second-order properties... provide non-parametric characterizations of the macro elasticities of substitution between factors and of the macro bias of technical change in terms of micro sufficient statistics. They allow us to generalize existing aggregation theorems and to derive new ones. We relate our results to the famous Cambridge-Cambridge controversy...

...Despite winning the battle, the English side arguably lost the war. Although exposed as a fiction, the “neoclassical” approach to modeling the production technology of an economy was nevertheless very useful. It was adopted and built upon by the real business cycle and growth literatures starting in the 1980s. Reports of the death of the aggregate production function turned out to be greatly exaggerated, as nearly all workhorse macroeconomic models now postulate an exogenous aggregate production function. Why did Robinson and Sraffa fail to convince macroeconomists to abandon aggregate production functions? One answer is the old adage: you need a model to beat a model.... Although the post-Keynesians were effective in dismantling this concept, they were not able to offer a preferable alternative.... Sraffa['s]... impact was limited.... In a world lacking both computational power and data, and in lieu of powerful theorems, it is little wonder that workaday macroeconomists decided to work with Solow’s parsimonious aggregate production function instead....

The aggregate cost function is defined as the solution of the dual planning problem which seeks to minimize the expenditure necessary to achieve real output Y given factor prices.... The first derivatives of the aggregate cost function are given by the sales shares of goods and factors.... The second derivatives of the aggregate cost function are determined by the elasticities of the sales shares of goods and factors...

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